Helping students make their own multiplication chartHelping Students make their own chart:

Links for Multiplication charts

www.math-aids.com

http://www.mathsisfun.com/multiplication-table-bw.html

http://www.helpingwithmath.com/printables/tables_charts/cha0301multiplication144.htm

Words in Math that are clues to operation required…..

Symbol Words Used

+Addition, Add, Sum, Plus, Increase, Total, All together

-Subtraction, Subtract, Minus, Less, Difference, Decrease, Take Away, Deduct

×Multiplication, Multiply, Product, By, Of,Times, Lots Of, All Together

÷Division, Divide, Quotient, Goes Into, How Many Times, Groups of, Goes into

Divisibility Rules 2 - 3

Divisible by 2 IFThe last digit is even (0,2,4,6,8)

Example:128 is129 is not

∞∞∞∞Divisible by 3 IF

The sum of the digits is divisible by 3Example:

381 (3+8+1=12, and 12÷3 = 4) Yes217 (2+1+7=10, and 10÷3 = 3 1/3) No

Divisibility Rules 4 - 5

DIVISIBLE BY 4 IF The last 2 digits are divisible by 4

EXAMPLE1312 is (12÷4=3)

7019 is not∞∞∞∞

DIVISIBLE BY 5 IF The last digit is 0 or 5

EXAMPLE: 175 is AND 809 is not∞∞∞∞

Divisibility Rules 6 - 7

DIVISIBLE BY 6 IF The number is divisible by both 2 and 3

114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes

308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No

∞∞∞∞

DIVISIBLE by 7 IFIf you double the last digit and subtract it from the rest of the number and the

answer is: 0, or divisible by 7 (Note: you can apply this rule to that answer again if you want)

672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7) No

∞∞∞∞

Divisibility Rules 8 - 9

DIVISIBLE 8 IFThe last three digits are divisible by 8

109816 (816÷8=102) Yes216302 (302÷8=37 3/4) No

∞∞∞∞

DIVISIBLE 9 IFThe sum of the digits is divisible by 9

(Note: you can apply this rule to that answer again if you want)

1629 (1+6+2+9=18, and again, 1+8=9) Yes2013 (2+0+1+3=6) No

Divisibility Rules 10 - 12

DIVISIBLE BY 10 IFThe number ends in 0

220 is BUT 221 is not∞∞∞∞

DIVISIBLE BY 11 IF If you sum every second digit and then subtract all other digits and the

answer is: 0, or divisible by 11EXAMPLES: 1364 ((3+4) - (1+6) = 0) Yes 3729 ((7+9) - (3+2) = 11) Yes

25176 ((5+7) - (2+1+6) = 3) No∞∞∞∞

DIVISIBLE BY 12 IFThe number is divisible by both 3 and 4

EXAMPLE: 648 (By 3? 6+4+8=18 and 18÷3=6 Yes. By 4? 48÷4=12 Yes) Yes524 (By 3? 5+2+4=11, 11÷3= 3 2/3 No. Don't need to check by 4.) No

Divisibility Rules links

http://www.math-aids.com/Division/Divisibility_Test_Handout.html

http://www.helpingwithmath.com/by_subject/division/div_divisibility_rules.htm

Common & Least Common Multiples

A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, ....

The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.

Least Common Multiples

Least Common Multiple

The least common multiple, or LCM, is another number that's useful in solving many math

problems. Let's find the LCM of 30 and 45. One way to find the least common multiple of two

numbers is to first list the prime factors of each number.

30 = 2 × 3 × 545 = 3 × 3 × 5

Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

2: one occurrence 3: two occurrences 5: one occurrence

2 × 3 × 3 × 5 = 90 <— LCM

After you've calculated a least common multiple, always check to be sure your answer can be divided evenly by both numbers.

EXAMPLES

3, 9, 21 Solution: List the prime factors of each.

3: 3 9: 3 × 3 21: 3 × 7

Multiply each factor the greatest number of times it occurs in any of the numbers. 9 has two 3s, and 21 has one 7, so we multiply 3 two times, and 7 once. This gives us 63, the smallest number that can be divided evenly by 3, 9, and 21. We check our

work by verifying that 63 can be divided evenly by 3, 9, and 21.∞∞∞∞

12, 80 Solution: List the prime factors of each.

12: 2 × 2 × 3 80: 2 × 2 × 2 × 2 × 5 = 80

Multiply each factor the greatest number of times it occurs in either number. 12 has one 3, and 80 has four 2's and one 5, so we multiply 2 four times, 3 once, and five

once. This gives us 240, the smallest number that can be divided by both 12 and 80. We check our work by verifying that 240 can be divided by both 12 and 80

Find the LCM with a calculator!!

http://www.calculatorsoup.com/calculators/math/lcm.php

Finding Equivalent Fractions:

Equivalent Fraction Links

http://www.dr-mikes-math-games-for-kids.com/equivalent-fractions-calculator.html

http://www.helpwithfractions.com/fraction-calculator/

Teaching Squares and Square Roots

Squares and Square Roots

Fact Family

Fact Family

The numbers along the left side and top are factors. The numbers inside are products

To use the multiplication table to find the product of 3 and 9, locate 3 in the first column and then find 9 in the top row.

Follow the 3 row to where it meets the 9 column. The number in the square where the column and row meet is the product.

See the shaded area in the table below.3 x 9 = 27

Another way to find the product of 3 and 9 on the multiplication table is to locate 9 in the first column and then 3 in the top row. See the shaded area in the table below.3 x 9 = 27

A multiplication table can also be used to find missing factors in multiplication and division sentences. Finding a missing factor in multiplication is similar to

finding a quotient in division.

Use the multiplication table below to find the missing factor in5 x n = 20.Locate 5 in the first column and move across the row to 20. The number in the square at the top of the column is the missing factor.5 x 4 = 20

To find the quotient in 20 ÷ 5 = n, follow the same steps as for 5 x 4 = 20 above. The number in the square at the left end of the row is the quotient.

20 ÷ 5 = 4

Making the connection between missing factors

in multiplication sentences and

quotients in division will help students better

understand the relationship between the two operations.

A multiplication table can also be used to reinforce students' understanding of other math concepts, such as the Commutative Property of Multiplication

and inverse operations. Look at the multiplication table below.

The table shows 3 x 6 = 18. It also shows 6 x 3 = 18

Because the Commutative Property of Multiplication

states that changing the order of the factors does not change the product.

The inverse, or opposite, of multiplication is division. So the table also shows

18 ÷ 3 = 6 and 18 ÷ 6 = 3. These four number sentences each use the same

three numbers: 3, 6, and 18.

Related number sentences that use the same numbers are

called a fact family

Some fact families have only two related number sentences. The multiplication table below shows the fact family for 7 and 49.

The fact family for 7 and 49 is 7 x 7 = 49 and

49 ÷ 7 = 7. There is only one multiplication

sentence in this fact family because the factors are the same number. There is only

one division sentence because the divisor and quotient are the same

number.

http://www.vertex42.com/Files/pdfs/2/school-reward-chart.pdf

Click the link above.

The progress chart can be printed and used to graph

goals in math.